M8N1: Students will understand different representations of numbers including square roots, exponents, and scientific notation.

M8N1.a: Find square roots of perfect squares.

Square Roots

M8N1.b: Recognize the (positive) square root of a number as a length of a side of a square with a given area.

Square Roots

M8N1.c: Recognize square roots as points and as lengths on a number line.

Square Roots

M8N1.d: Understand that the square root of 0 is 0 and that every positive number has two square roots that are opposite in sign.

Square Roots

M8N1.e: Recognize and use the radical symbol to denote the positive square root of a positive number.

Simplifying Radicals - Activity A
Square Roots

M8N1.f: Estimate square roots of positive numbers.

Square Roots

M8N1.g: Simplify, add, subtract, multiply, and divide expressions containing square roots.

Operations with Radical Expressions
Square Roots

M8N1.i: Simplify expressions containing integer exponents.

Dividing Exponential Expressions
Exponents and Power Rules

M8N1.k: Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation.

Square Roots

M8G1: Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence.

M8G1.a: Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.

Construct Parallel and Perpendicular Lines

M8G1.b: Apply properties of angle pairs formed by parallel lines cut by a transversal.

Investigating Angle Theorems - Activity A

M8G1.c: Understand the properties of the ratio of segments of parallel lines cut by one or more transversals.

Investigating Angle Theorems - Activity A

M8G1.d: Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.

Congruence in Right Triangles

M8G2: Students will understand and use the Pythagorean theorem.

M8G2.a: Apply properties of right triangles, including the Pythagorean theorem.

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity B

M8G2.b: Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

M8A1: Students will use algebra to represent, analyze, and solve problems.

M8A1.a: Represent a given situation using algebraic expressions or equations in one variable.

Using Algebraic Equations

M8A1.b: Simplify and evaluate algebraic expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

M8A2: Students will understand and graph inequalities in one variable.

M8A2.a: Represent a given situation using an inequality in one variable.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

M8A2.b: Use the properties of inequality to solve inequalities.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

M8A2.c: Graph the solution of an inequality on a number line.

Compound Inequalities
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

M8A3: Students will understand relations and linear functions.

M8A3.a: Recognize a relation as a correspondence between varying quantities.

Introduction to Functions

M8A3.b: Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

M8A3.c: Distinguish between relations that are functions and those that are not functions.

Introduction to Functions
Linear Functions

M8A3.d: Recognize functions in a variety of representations and a variety of contexts.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Using Tables, Rules and Graphs

M8A3.e: Use tables to describe sequences recursively and with a formula in closed form.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions
Using Tables, Rules and Graphs

M8A3.f: Understand and recognize arithmetic sequences as linear functions with wholenumber input values.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Slope-Intercept Form of a Line - Activity A

M8A3.g: Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

M8A3.h: Identify relations and functions as linear or nonlinear.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

M8A3.i: Translate among verbal, tabular, graphic, and algebraic representations of functions.

Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

M8A4: Students will graph and analyze graphs of linear equations.

M8A4.a: Interpret slope as a rate of change.

Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B

M8A4.b: Determine the meaning of the slope and y-intercept in a given situation.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

M8A4.c: Graph equations of the form y = mx + b.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

M8A4.d: Graph equations of the form ax + by = c.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

M8A4.e: Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.

Defining a Line with Two Points
Function Machines 2 (Functions, Tables, and Graphs)
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

M8A5: Students will understand systems of linear equations and use them to solve problems.

M8A5.b: Solve systems of equations graphically and algebraically, using technology as appropriate.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

M8D2: Students will determine the number of outcomes related to a given event.

M8D2.a: Use tree diagrams to find the number of outcomes.

Permutations
Permutations and Combinations

M8D3: Students will use the basic laws of probability.

M8D3.a: Find the probability of simple, independent events.

Compound Independent Events
Compound Independent and Dependent Events
Spin the Big Wheel! (Probability)

M8D3.b: Find the probability of compound, independent events.

Compound Independent Events
Compound Independent and Dependent Events

M8D4.a: Gather data that can be modeled with a linear function.

Function Machines 2 (Functions, Tables, and Graphs)

M8D4.b: Estimate and determine a line of best fit from a scatter plot.

Correlation
Lines of Best Fit Using Least Squares - Activity A